# Current students

Unit outline_

## Overview

This unit will study basic concepts and methods of time series analysis applicable in many real world problems applicable in numerous fields, including economics, finance, insurance, physics, ecology, chemistry, computer science and engineering. This unit will investigate the basic methods of modelling and analyzing of time series data (ie. Data containing serially dependence structure). This can be achieved through learning standard time series procedures on identification of components, autocorrelations, partial autocorrelations and their sampling properties. After setting up these basics, students will learn the theory of stationary univariate time series models including ARMA, ARIMA and SARIMA and their properties. Then the identification, estimation, diagnostic model checking, decision making and forecasting methods based on these models will be developed with applications. The spectral theory of time series, estimation of spectra using periodogram and consistent estimation of spectra using lag-windows will be studied in detail. Further, the methods of analyzing long memory and time series and heteroscedastic time series models including ARCH, GARCH, ACD, SCD and SV models from financial econometrics and the analysis of vector ARIMA models will be developed with applications. By completing this unit, students will develop the essential basis for further studies, such as financial econometrics and financial time series. The skills gain through this unit of study will form a strong foundation to work in a financial industry or in a related research organization.

### Unit details and rules

Academic unit Mathematics and Statistics Academic Operations 6 STAT2X11 and (MATH1062 or MATH1962 or MATH1972 or MATH1X03 or MATH1907 or MATH1X23 or MATH1933) None STAT4025 None Yes

### Teaching staff

Coordinator Shelton Peiris, shelton.peiris@sydney.edu.au Eugene Seneta

## Assessment

The census date for this unit availability is 2 April 2024
Type Description Weight Due Length
Supervised exam

Final Exam
60% Formal exam period 2 hours
Outcomes assessed:
Small test Comp A
weekly computer reports worth 4%. In-class R quiz (CQ1) in week 7 worth 6%.
10% Multiple weeks
Due date: 08 Apr 2024 at 12:00
one hour
Outcomes assessed:
Small test Comp B
weekly computer reports 4%. In-class R quiz (CQ2) in week 13 worth 6%
10% Multiple weeks
Due date: 20 May 2024 at 12:00
one hour
Outcomes assessed:
Small test Quiz 1
In-class quiz worth 10%
10% Week 08
Due date: 15 Apr 2024 at 18:00
one hour
Outcomes assessed:
Small test Quiz 2
In-class quiz worth 10%
10% Week 13
Due date: 24 May 2024 at 12:00
one hour
Outcomes assessed:

### Assessment summary

• Quiz 1: This is a closed book quiz (pen and paper). You are allowed to bring  a University approved non-programmable calculator and/or R. This will be done in-class in week 8 during your lecture time on Monday 15 April at 17.00 and submit by 18.00, worth 10%.
• Comp A: This consists of 2 subcomponents during Weeks 2-7: online submission of weekly reports worth 4% and a Computer quiz1 (CQ1) in week 7 (Monday 8 April) at 11.00 and submit by 12.00 (pen and paper) is worth 6%. The CQ1 is an in-class, closed book computer exam/quiz. This must be done in your assigned computer class time on Monday.
• Quiz 2: This is a closed book quiz (pen and paper). You are allowed to bring a University approved non-programmable calculator and/or R during this quiz. This will be done in week13 during your tutorial time on Friday 24 May and submit by 12.00. Worth 10%.
• Comp B: This consists of 2 subcomponents during Weeks 8-13: online submission of computer reports worth 4% and a Computer quiz2 (CQ2) in week 13, Monday 20 May at 11.00 submit by 12.00 (pen and paper) is worth 6%. This CQ2 is an in-class, closed book computer exam/quiz. This must be done in your assigned computer class on Monday.
• Final exam: This is in the Final exam period. If a second replacement exam is required, this exam may be delivered via an alternative assessment method, such as a viva voce (oral exam). The alternative assessment will meet the same learning outcomes as the origina exam. The format of the alternative assessment will be determined by the unit coordinator.

Detailed information for each assessment can be found on Canvas.

### Assessment criteria

The University awards common result grades, set out in the Coursework Policy 2014 (Schedule 1).

As a general guide, a high distinction indicates work of an exceptional standard, a distinction a very high standard, a credit a good standard, and a pass an acceptable standard.

Result name

Mark range

Description

High distinction

85 - 100

Distinction

75 - 84

Credit

65 - 74

Pass

50 - 64

Fail

0 - 49

When you don’t meet the learning outcomes of the unit to a satisfactory standard.

### Late submission

In accordance with University policy, these penalties apply when written work is submitted after 11:59pm on the due date:

• Deduction of 5% of the maximum mark for each calendar day after the due date.
• After ten calendar days late, a mark of zero will be awarded.

The Current Student website  provides information on academic integrity and the resources available to all students. The University expects students and staff to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.

We use similarity detection software to detect potential instances of plagiarism or other forms of academic integrity breach. If such matches indicate evidence of plagiarism or other forms of academic integrity breaches, your teacher is required to report your work for further investigation.

You may only use artificial intelligence and writing assistance tools in assessment tasks if you are permitted to by your unit coordinator, and if you do use them, you must also acknowledge this in your work, either in a footnote or an acknowledgement section.

Studiosity is permitted for postgraduate units unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission.

## Learning support

### Simple extensions

If you encounter a problem submitting your work on time, you may be able to apply for an extension of five calendar days through a simple extension.  The application process will be different depending on the type of assessment and extensions cannot be granted for some assessment types like exams.

### Special consideration

If exceptional circumstances mean you can’t complete an assessment, you need consideration for a longer period of time, or if you have essential commitments which impact your performance in an assessment, you may be eligible for special consideration or special arrangements.

Special consideration applications will not be affected by a simple extension application.

### Using AI responsibly

Co-created with students, AI in Education includes lots of helpful examples of how students use generative AI tools to support their learning. It explains how generative AI works, the different tools available and how to use them responsibly and productively.

### Support for students

The Support for Students Policy 2023 reflects the University’s commitment to supporting students in their academic journey and making the University safe for students. It is important that you read and understand this policy so that you are familiar with the range of support services available to you and understand how to engage with them.

The University uses email as its primary source of communication with students who need support under the Support for Students Policy 2023. Make sure you check your University email regularly and respond to any communications received from the University.

Learning resources and detailed information about weekly assessment and learning activities can be accessed via Canvas. It is essential that you visit your unit of study Canvas site to ensure you are up to date with all of your tasks.

If you are having difficulties completing your studies, or are feeling unsure about your progress, we are here to help. You can access the support services offered by the University at any time:

Support and Services (including health and wellbeing services, financial support and learning support)

## Weekly schedule

WK Topic Learning activity Learning outcomes
Week 01 1. Time series data, components of a time series; 2. Filtering to remove trends and seasonal components. Review of R with basic commands. Lecture and tutorial (5 hr)
Week 02 1. Stationarity time series; 2. Autocorrelation function (ACF) and Partial autocorrelation function (PACF) and their properties; 3. Sample autocorrelations and partial autocorrelations; 4. White noise process and Probability models for stationary time series. Lecture and tutorial (4 hr)
1. Stationarity time series; 2. Autocorrelation function (ACF) and Partial autocorrelation function (PACF) and their properties; 3. Sample autocorrelations and partial autocorrelations; 4. White noise process and Probability models for stationary time series. Computer laboratory (1 hr)
Week 03 1. Moving Average (MA) models and properties; 2. Invertibility of MA models; 3. Autoregressive (AR) models and their properties; 4. Stationarity of AR models Lecture and tutorial (4 hr)
1. Moving Average (MA) models and properties; 2. Invertibility of MA models; 3. Autoregressive (AR) models and their properties; 4. Stationarity of AR models Computer laboratory (1 hr)
Week 04 1. Mixed Autoregressive Moving Average (ARMA) models and their properties; 2. Homogeneous nonstationary time series (HNTS). Simple models for HNTS; 3. Autoregressive Integrated Moving Average (ARIMA) models and related results; 4. Review of theoretical patterns of ACF and PACF for AR, MA and ARMA processes; 5. Identification of possible AR, MA, ARMA and ARIMA models for a set of time series data Lecture and tutorial (4 hr)
1. Mixed Autoregressive Moving Average (ARMA) models and their properties; 2. Homogeneous nonstationary time series (HNTS). Simple models for HNTS; 3. Autoregressive Integrated Moving Average (ARIMA) models and related results; 4. Review of theoretical patterns of ACF and PACF for AR, MA and ARMA processes; 5. Identification of possible AR, MA, ARMA and ARIMA models for a set of time series data Computer laboratory (1 hr)
Week 05 1. Estimation and fitting ARIMA models via MM and MLE methods; 2. Hypothesis testing, diagnostic checking and goodness-of-fit tests. AIC for ARIMA models; 3. Introduction to forecasting methods for ARIMA models Lecture and tutorial (4 hr)
1. Estimation and fitting ARIMA models via MM and MLE methods; 2. Hypothesis testing, diagnostic checking and goodness-of-fit tests. AIC for ARIMA models; 3. Introduction to forecasting methods for ARIMA models Computer laboratory (1 hr)
Week 06 1. Minimum mean square error (mmse) forecasting and its properties; 2. Derivation of l-step ahead mmse forecast function. Forecast updates; 3. Forecast errors, related results and applications Lecture and tutorial (4 hr)
1. Minimum mean square error (mmse) forecasting and its properties; 2. Derivation of l-step ahead mmse forecast function. Forecast updates; 3. Forecast errors, related results and applications Computer laboratory (1 hr)
Week 07 1. An introduction to spectral theory of time series; 2. Spectral density function (sdf) of an ARMA model; 3. Examples Lecture and tutorial (4 hr)
1. An introduction to spectral theory of time series; 2. Spectral density function (sdf) of an ARMA model; 3. Examples Computer laboratory (1 hr)
Week 08 1. Estimation of the sdf using the periodogram; 2. Sampling properties of the periodogram; 3. Smoothed periodogram estimators for the sdf Lecture and tutorial (4 hr)
1. Estimation of the sdf using the periodogram; 2. Sampling properties of the periodogram; 3. Smoothed periodogram estimators for the sdf Computer laboratory (1 hr)
Week 09 1. An introduction to fractional differencing and long memory time series modelling; 2. Estimation of ARFIMA(p,d,q); 3. Applications of ARFIMA Lecture and tutorial (4 hr)
1. An introduction to fractional differencing and long memory time series modelling; 2. Estimation of ARFIMA(p,d,q); 3. Applications of ARFIMA Computer laboratory (1 hr)
Week 10 1. Generalised fractional processes. Gegenbaur processes; 2. Spectral properties of Gegenbauer processes; 3. Estimation of parameters of Gegenbauer models Lecture and tutorial (4 hr)
1. Generalised fractional processes. Gegenbaur processes; 2. Spectral properties of Gegenbauer processes; 3. Estimation of parameters of Gegenbauer models Computer laboratory (1 hr)
Week 11 1. Topics from financial time series/econometrics: Conditional heteroscedasticity; 2. ARCH, GARCH processes for heavy tailed data and their properties; 3. Stochastic volatility models and their properties Lecture and tutorial (4 hr)
1. Topics from financial time series/econometrics: Conditional heteroscedasticity; 2. ARCH, GARCH processes for heavy tailed data and their properties; 3. Stochastic volatility models and their properties Computer laboratory (1 hr)
Week 12 An introduction to VAR and vector ARIMA models. Spectral properties. Estimation. Lecture and tutorial (4 hr)
An introduction to VAR and vector ARIMA models. Spectral properties. Estimation. Computer laboratory (1 hr)
Week 13 State-space models and their properties. Quasi Maximum Likelihood Estimation (QMLE) Lecture and tutorial (4 hr)
State-space models and their properties. Quasi Maximum Likelihood Estimation (QMLE) Computer laboratory (1 hr)

### Attendance and class requirements

Due to the exceptional circumstances caused by the COVID-19 pandemic, attendance requirements for this unit of study have been amended. Where online tutorials/workshops/virtual laboratories have been scheduled, students should make every effort to attend and participate at the scheduled time. Penalties will not be applied if technical issues, etc. prevent attendance at a specific online class. In that case, students should discuss the problem with the coordinator, and attend another session, if available.

### Study commitment

Typically, there is a minimum expectation of 1.5-2 hours of student effort per week per credit point for units of study offered over a full semester. For a 6 credit point unit, this equates to roughly 120-150 hours of student effort in total.

1. Analysis of Financial Time Series, R.S.Tsay, John Wiley 3rd Edition (2010).
2. The Analysis of Time Series: An Introduction with R, Chris Chatfield, Haipeng Xing, Chapman and Hall/CRC, 7th Edition (2019).

## Learning outcomes

Learning outcomes are what students know, understand and are able to do on completion of a unit of study. They are aligned with the University's graduate qualities and are assessed as part of the curriculum.

At the completion of this unit, you should be able to:

• LO1. 1.Explain and examine time series data and identify components of a time series; remove trends, seasonal and other components.
• LO2. Identify stationarity time series; sample autocorrelations and partial autocorrelations, probability models for stationary time series.
• LO3. Explain homogeneous nonstationary time series, simple and integrated models and related results.
• LO4. Apply estimation and fitting methods for ARIMA models via MM and MLE methods.
• LO5. Apply hypothesis testing, diagnostic checking and goodness-of-fit tests methodology.
• LO6. Construct forecasting methods for ARIMA models.
• LO7. Explain spectral methods in time series analysis.
• LO8. Apply financial time series and related models to straightforward problems.
• LO9. Apply the methods of analysis of GARCH and other models for volatility.
• LO10. Explain and apply methods of vector time series models

The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course. As a future Sydney graduate, the set of qualities have been designed to equip you for the contemporary world.

 GQ1 Depth of disciplinary expertise Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline. GQ2 Critical thinking and problem solving Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem. GQ3 Oral and written communication Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context. GQ4 Information and digital literacy Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies. GQ5 Inventiveness Generating novel ideas and solutions. GQ6 Cultural competence Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures. In the Australian context, this includes and celebrates Aboriginal and Torres Strait Islander cultures, knowledge systems, and a mature understanding of contemporary issues. GQ7 Interdisciplinary effectiveness Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries. GQ8 Integrated professional, ethical, and personal identity An integrated professional, ethical and personal identity is understanding the interaction between one’s personal and professional selves in an ethical context. GQ9 Influence Engaging others in a process, idea or vision.

### Outcome map

GQ1 GQ2 GQ3 GQ4 GQ5 GQ6 GQ7 GQ8 GQ9

## Responding to student feedback

This section outlines changes made to this unit following staff and student reviews.

### Work, health and safety

We are governed by the Work Health and Safety Act 2011, Work Health and Safety Regulation 2011 and Codes of Practice. Penalties for non-compliance have increased. Everyone has a responsibility for health and safety at work. The University’s Work Health and Safety policy explains the responsibilities and expectations of workers and others, and the procedures for managing WHS risks associated with University activities.

General Laboratory Safety Rules

• No eating or drinking is allowed in any laboratory under any circumstances
• A laboratory coat and closed-toe shoes are mandatory